It is well known that signal detectors which operate digitally are generally built around the basic digital apparatus called digital filter. Tone signal detectors used in telephony are a good example. Such a filter is designed to function as a band-pass, low-pass or high-pass filter etc. to pass or to block a signal containing a desired frequency component. For example, in digital telephony there are vast areas where detecting a specific tone signal is required for performing a variety of telephone operations. Various kinds of digital filters have been used for these purposes. U.S. Pat. No. 4,354,248, issued Oct. 12, 1982 to Conger et al, describes a programmable multi-frequency tone receiver using such a digital filter technique. The tone receiver uses a time multiplexed digital filter consisting of three cascaded second order filters under control of a sequence controller. It is very complex and requires a large amount of memory capacity. U.S. Pat. No. 3,777,130, issued Dec. 4, 1973 to Croisier et al, teaches a general purpose digital filter for PCM encoded signals. It describes a novel way of implementing into hardware a digital filter for binary coded signals. It takes advantage of the use of modified two's complement numeric representation and results in a significant saving of the memory spaces in the storage device. U.S. Pat. No. 4,797,846, issued Jan. 10, 1989 to Benkara et al, is directed to a digital filter apparatus with resonance characteristics. This patent discloses a straightforward scheme of implementation which needs less hardware. It teaches specifically selected values of coefficient factors which simplify hardware implementation. U.S. Pat. No. 4,450,533, issued May 22, 1984 to Petit et al, discloses digital processing apparatus which is hardware implemented according to the distributed arithmetic concept. A detailed discussion on the distributed arithmetic concept used for the hardware realization of digital filters is found in IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. ASSP-22, No. 6, December 1974, entitled "A New Hardware Realization of Digital Filters", by A. Peled and B. Liu. The present invention further reduces the hardware requirement for digital signal processing apparatus using this concept.